Nonlinear mass sensors based on electronic feedback and methods of using the same

ABSTRACT

A device and method for sensing including a sensor having a functional surface layer located to interact with a material to be sensed, the sensor having an output that produces a signal responsive one or more of inertia, stiffness, acceleration, pressure, radiation, chemical compounds, and biological compounds; and further including electronics including: an input coupled to the sensor to receive a first signal therefrom; and a non-linearity provider that applies one or more non-linear operations to the input signal to generate a non-linear second signal.

PRIORITY

The present application is a non-provisional application of U.S.Provisional Application 62/093,747 filed Dec. 18, 2014, titled“NONLINEAR MASS SENSORS BASED ON ELECTRONIC FEEDBACK AND METHODS OFUSING THE SAME,” the priority of which is hereby claimed and thedisclosure of which is hereby incorporated by reference.

STATEMENT REGARDING GOVERNMENT FUNDING

This invention was made with government support under 2013-ST-061-ED0001awarded by the U.S. Department of Homeland Security. The government hascertain rights in the invention.

TECHNICAL FIELD

This disclosure relates to sensors capable of sensing mass, stiffness,and chemical or biological substances.

BACKGROUND AND SUMMARY

To date, many vibration-based sensing modalities have relied uponmonitoring small shifts in the natural frequency of a system to detectstructural changes (e.g. in mass or stiffness), which are attributableto the chemical, biological, or other types of phenomenon that are beingmeasured. Often, this approach carries significant signal processingexpense, due to the presence of electronics such as precision phaselocked loops, when high sensitivities are required.

Microelectromechanical systems (MEMS) based sensing is an important areaof transducer development and has been so for the past several decades.This importance stems from its potential to provide low-cost, scalable,and sensitive sensor alternatives based upon a wide variety ofmodalities. Resonant mode sensing is common in MEMS devices and isfounded on correlating changes in the resonant behavior of structuresand devices to identifiable parameter changes. Traditional methods inthis area rely on linear or pseudo-linear sensing, which, in turn, relyon a shift in resonant frequencies of a vibrating structure to detectchanges, either in the device structure or its surroundings. Thesemethods have been successfully used to detect a number of chemical andother small masses (picograms and smaller in many cases), and have alsofound use in applications such as atomic force microscopy (AFM). It isimportant to note, however, that performing sensing in the linear modewith high sensitivity requires careful system design and may requiresignificant cost or complexity to implement. It may require phase-lockedloops, lock-in amplifiers, or other specialized equipment to perform themeasurements and yield high sensitivity in frequency shift measurement.

Bifurcation-based mass sensing, on the other hand, is an approach tomass sensing that relies upon nonlinear behavior to produce largechanges in amplitude when a mass change threshold is exceeded. Previoussuccessful sensing efforts using bifurcation-based sensing have achievedhigh sensitivity albeit with the tradeoff being that the methods usuallydo not measure mass in a quantifiable manner aside from a certainthreshold being exceeded.

Many microscale resonator devices capable of operating in a nonlinearregime commonly exhibit classical Duffing-like frequency responses.These devices can exhibit multiple coexisting steady-state solutions(stable and unstable), saddle-node bifurcations, and hystereticbehavior. A potential disadvantage to the state of the art inbifurcation-based sensing in microscale devices is the fact that in manycases the systems must be driven with magnitudes of excitation that maydamage the device (18 V peak-to-peak excitation was required, where thedevice has a nominal breakdown voltage of 10 V). It is also worth notingthat it may be possible to compensate for this by redesigning devicesspecifically for bifurcation-based sensing, but this may not beeconomical or practical for all applications (higher drive amplitudesrequire higher power circuitry to function, and this reducesapplicability for battery powered, low power, mobile sensing).

One approach to tackling the aforementioned issue is to use feedback toproduce a bifurcation at lower drive amplitudes. Prior work in this areahas a bistable system structure rather than that of a Duffing resonator,but also had the disadvantage of the vibration actuation being separate(non-collocated). Likewise, nonlinear feedback methods have beensuggested for use in MEMS devices in the past, but generally forreduction or elimination of nonlinear behavior. Notably the majority ofthis work has been performed either in simulation or on relativelylow-frequency, macro-scale analogs of MEMS systems.

Most small-scale resonant sensor designs utilize linear phenomena forsensing. Specifically, they utilize chemomechanically-induced changes inmass or stiffness, to induce a change in resonant frequency and thussignal a detection event. These systems have proven utility inlaboratory settings, but have not transferred to real-world, portablesensing applications, due to hardware constraints and the fixedsensitivity of the devices.

Thus a need exists for a sensors that can sense mass, stiffness, andchemical or biological substances which are more sensitive and tunable.It also desirable to have such sensing approaches allow forsignificantly reduced costs, improved reliability and enhancedrobustness. It is further desirable to have sensing approaches thateliminate the need for customized mechanical/electrical designs.

According to a first embodiment of the present disclosure, a sensingdevice is provided including: a sensor having a functional surface layerlocated to interact with a material to be sensed, the sensor having anoutput that produces a signal responsive one or more of inertia,stiffness, acceleration, pressure, radiation, chemical compounds, andbiological compounds; and further including electronics including: aninput coupled to the sensor to receive a first signal therefrom; and anon-linearity provider that applies one or more non-linear operations tothe input signal to generate a non-linear second signal.

According to another embodiment of the present disclosure, a method ofgenerating a non-linear sensor response is provided including: obtaininga first signal from a sensor having a functional surface layer locatedto interact with a material to be sensed, the sensor having an outputthat produces a signal responsive one or more of inertia, stiffness,acceleration, pressure, radiation, chemical compounds, and biologicalcompounds; and applying one or more non-linear electrical operations,including a first operation, to the first signal to generate anon-linear second signal.

According to another embodiment of the present disclosure, a computerreadable media having non-transitory instructions thereon is provided,that when interpreted by a processor cause the processor to: obtain afirst signal from a sensor having a functional surface layer located tointeract with a material to be sensed, the sensor having an output thatproduces a signal responsive one or more of inertia, stiffness,acceleration, pressure, radiation, chemical compounds, and biologicalcompounds; and apply one or more non-linear electrical operations,including a first operation, to the first signal to generate anon-linear second signal.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows examples of softening- and hardening-type Duffing resonatormagnitude-frequency response curves;

FIG. 2a shows an Epson FC-135 quartz tuning fork device

FIG. 2b shows an Abracon AB38T quartz tuning fork device;

FIG. 3 is a schematic representation of the design concept;

FIG. 4 shows an implementation of the design according to the presentdisclosure;

FIG. 5 is a detailed circuit diagram of an implementation of the design;

FIG. 6 is a demonstration of the tuning of the Duffing-like bifurcationresponse, with both hardening and softening characteristics;

FIG. 7 is a demonstration of the tuning of the Duffing-like frequencyresponse in the softening feedback mode, with a fixed gain andincreasing excitation amplitude;

FIG. 8 is a demonstration of the tuning of the Duffing-like frequencyresponse in the hardening feedback mode, with fixed gain and increasingexcitation amplitude;

FIG. 9 shows softening responses of three different AB38T tuning forkcrystal devices, with their respective linear responses also shown;

FIG. 10 is a demonstration of tuning of Duffing-like frequency responsein the softening mode for the Epson FC-135 tuning fork crystal, with afixed gain and increasing excitation amplitude; and

FIG. 11 is a flowchart showing exemplary operation of a method ofoperating they systems of any of the previous FIGS.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thepresent disclosure, reference will now be made to the embodimentsillustrated in the drawings, and specific language will be used todescribe the same. It will nevertheless be understood that no limitationof the scope of this disclosure is thereby intended.

This disclosure details a new approach, based on nonlinear electronicfeedback, through which conventional crystal resonator (e.g., quartztuning forks) and related hardware, can be re-purposed as nonlinearmass, chemical, or biological sensors. The approach complementsbifurcation-based sensing systems in that it retains the benefits ofearlier systems over conventional, small-scale resonant sensor designs(including simplified electronics and high and tunable sensitivity), andfurthers it by allowing for significantly reduced costs, improvedreliability and enhanced robustness.

The above mentioned methods and systems find applicability in a varietyof detection applications, some non-limiting examples of which are masssensors, chemical sensors, and biosensors. The sensor systems describedhere can be configured for a variety of applications. As a non-limitingexample, the sensors of this disclosure can be configured for tracevapor explosives detection.

The present work demonstrates a method for producing a tunablebifurcation in a system that would otherwise be well characterized witha linear model. The bifurcation used is that which arises in thefrequency response of Duffing resonators, namely a saddle-node orcyclic-fold, and this method uses a very low cost device (quartz crystaltuning fork resonator) as the platform for demonstration. This device isa piezoelectric device, and thus, collocated actuation and sensing ofthe vibrational behavior is possible and relatively straightforward toachieve. The device requires a relatively high-frequency of operation toimplement a nonlinear feedback loop. Furthermore, standard digitalcontrol methods have significant disadvantages at such frequencies,especially from an implementation cost and phase-lag perspective. Inorder to show practical implementation on a class of devices thatoperates at the high frequencies typical of many MEMS devices, an analogfeedback loop consisting of operational amplifiers, passive components,and multipliers capable of providing the cubic nonlinearity used toproduce the bifurcation behavior with minimal phase lag are employed.Finally, the sensitivity and bifurcation points of the device are shownto be tunable via control of the feedback gain and the overallexcitation amplitude. The type of Duffing-like response (hardening orsoftening) is made selectable, allowing for a versatile platformsuitable for future Duffing-like bifurcation-based devices. Furthermore,while the present disclosure discusses primarily feedback systems, itshould be understood that embodiments are envisioned where the providedresponse is achieved through feed-forward systems that repeat processingoperations or apply different processing operations.

Design Concept

A) Sensing Strategy: Bifurcation-based mass sensing relies uponnonlinear behavior to produce large changes in amplitude when a masschange threshold is exceeded. Duffing resonators have a characteristicfrequency response which qualitatively depends on whether the resonatoris hardening or softening as shown in FIG. 1. When performing afrequency sweep on a softening-type Duffing resonator, when thefrequency is increasing, the system follows one trajectory until thebifurcation frequency, and then it jumps to the other stable trajectory.This occurs when the frequency is decreased as well, but the jumpfrequencies are different for the increasing and decreasing cases. Ifthe excitation frequency is just below the bifurcation frequency, andthe mass of the device increases, the bifurcation frequency decreases,and if it passes the excitation frequency, a jump event will occur. Thisis the premise of the sensing method.

B) Theory of Operation: The softening Duffing resonator is a suitablemodel to approximate the dynamics of a real system suitable for sensing.Duffing resonators have a characteristic frequency response whichqualitatively depends on whether the resonator is hardening or softeningas shown in FIG. 1.

In the present implementation, the demonstration device is a quartztuning fork, a class of devices that is well-studied due to its use intiming devices, as well as in linear mass sensing and AFM applications.They are low cost due to being mass-produced, and have relatively tighttolerances and repeatability in a number of aspects of theirfabrication. Two examples of quartz tuning fork devices are shown inFIG. 2. Considering the model of a quartz tuning fork crystal resonatoras discussed in literature, the mechanical behavior of the crystal canbe described by:

M{umlaut over (x)}+h{dot over (x)}+kx=F(t).  (1)

Here, h is an equivalent damping term, M is an equivalent mass term, kis an equivalent stiffness term, x is the displacement (mechanical), andF (t) is the forcing term. This is a very simple second-order (linear)harmonic resonator model. It should apply to many possible devices, notjust the aforementioned tuning forks.

In order for the device to behave as a Duffing-type system, anonlinearity (such as a cubic non-linearity) is introduced. Thisnonlinearity can be added to the system via feedback, since F(t) isprescribed externally. Therefore, if F(t) is chosen such that

F=F*(t)−αx ³,  (2)

then the resulting system equation becomes:

M{umlaut over (x)}+h{dot over (x)}+kx+αx ³ =F*(t).  (3)

In this case, F*(t) will be a sinusoidal input A sin(ωt). The Duffingresponse can now be tuned by controlling the feedback gain α.

In order to measure the effective position of the sensor, x, thepiezoelectric nature of the device is exploited. The piezoelectriccharacteristics of the quartz material can also be used tosimultaneously provide the excitation to the device. Thus, the devicecan be driven by a summing amplifier that adds an input excitationV_(IN) (t) with the desired cubic feedback. The drive amplifier willexcite the crystal through a transimpedance circuit with high gain, toproduce a voltage proportional to the current passing through thecrystal due to the drive input. This voltage, V_(TI), is thereforeproportional to x. To produce a voltage proportional to x, VT I isintegrated, then passed through a high-pass filter (HPF) to eliminate DCoffset. Following the filtering, the output V_(X) is proportional to x,and the quantity is passed through two analog multipliers in order tocreate a value proportional to x³. This is passed through an inverter,and either the inverted cubed signal or the original cubed signal ispassed through a non-inverting gain amplifier to produce a voltageproportional to αx³ which is then summed into the input excitation tocomplete the feedback loop. The design schematic can be seen in FIG. 3.

Theoretically, the method detailed above should be applicable as eitheran analog or digital embodiments. However, such resonator systems andtheir nonlinear behavior are generally phase-sensitive. For slowersystems (in terms of natural frequency and bifurcation frequencies)digital design may be practical. However, for the crystals used in thissensing platform, with a resonant frequency close to 32.760 kHz,sampling at the “rule-of-thumb” of 20 times the nominal controlfrequency for feedback control applications would introduce a phase lagof approximately 18 degrees, which is quite significant, and wouldlikely not allow desired results. Even sampling at 100 times thefrequency would introduce 3.6 degrees of phase lag, assuming that theoutput can be produced within one sampling period. In addition, withoutcareful smoothing and filtering, DAC outputs may introduce quantizationnoise that may cause premature bifurcation. Therefore, from theperspective of design practicality, cost, and performance, an analogembodiment is discussed.

The design concept illustrated in FIG. 3 can be realized with discreteelectronic components, programmable electronic devices, applicationspecific integrated circuits (ASICs), micro-controllers and combinationof software/hardware implementations.

C): Design Guidelines: The circuit can be considered as having threemain subsystems: the actuation and sensing subsystem, the filteringsubsystem, and the (cubic) feedback generation. Frequency ranges andexcitation voltage ranges of interest depend on the device used as thesensing platform. As an example, most commercially available quartztuning forks range in operating frequency from 10 kHz to 200 kHz, whileother quartz resonators can operate up to the hundreds of MHz or higherrange (using overtones, and not in tuning fork geometries). Voltageranges of operation span from less than one volt to tens of volts.

The methodology discussed herein that is used to produce the bifurcationis applicable to a wide range of devices when one has direct controlover the sensing and actuation circuitry. The embodiment discussed bythe present disclosure provides design guidelines for working withpiezoelectric, collocated sensing and actuation devices.

Sensing and Actuation Subsystem: Collocated sensing and actuation is awell-studied area in structural mechanics and control, and in particularhas been very carefully studied in the area of AFM and scanning probemicroscopy (SPM) systems, where quartz tuning forks are used asactuation and sensing elements. One method of simultaneously driving andsensing the behavior of a piezoelectric device is that of driving itthrough a bridge circuit which can be either an active or passivebridge. As with most bridge circuits, tuning is generally required afterconstruction in order to get the desired performance out of the circuit,due to tolerances and parasitic capacitance and inductance. A feature ofthe active bridge circuit is the ability to remove the asymmetry presentin the frequency response that arises from the shunt capacitance as seenin the commonly-used Butterworth-Van Dyke model, along with providinghigh sensitivity and low noise. However, low noise and high sensing gaincan be achieved without the use of shunt capacitance compensation, ifone is willing to accept the asymmetry in the response. In the presentexemplary embodiment, a simple transimpedance amplifier configuration isused.

In order to design the transimpedance amplifier stage the equivalentseries resistance (ESR) of the device is characterized. The ESR is theequivalent impedance of the crystal resonator measured at the electricalresonant frequency. Based on the ESR (provided by the manufacturer ordetermined via impedance measurement), the approximate currentconsumption of the device (root-mean squared (RMS) should be sufficientfor this purpose) can be estimated for a given input voltage magnitude.The maximum current consumption should occur near electrical resonance.In order to provide a useful signal-to-noise ratio for later stages, atransimpedance gain (feedback resistor) can be chosen such that thevoltage output of the transimpedance stage uses a reasonable fraction(10% or more) of the dynamic range. Photodiode measurementtransimpedance circuits deal with a similar range of currents and designconsiderations for them are widely available—the same guidelines applyhere, with low input bias and input offset current being a used designparameter. The output of the transimpedance stage should drive thefiltering subsystem.

Filtering Subsystem:

As discussed previously, the filtering subsystem contains an integratorand a high-pass filter circuit. The integrator has a sufficiently widebandwidth for the system, with low distortion and the useful integrationfrequency range spanning at least a decade below the operating frequencyand allowing attenuated integration of the third harmonic. Integratordesign is a standard op amp design technique, as is high-pass filterdesign. The design uses an operational amplifier with a low input offsetvoltage but sufficient bandwidth to meet requirements.

Nonlinear Feedback Subsystem:

The nonlinear feedback subsystem consists of gain and/or attenuationcircuits, the circuitry to produce the, exemplary, cubic signal, andfinally the summing amplifier which adds together the excitation and thenonlinear feedback. Gain and attenuation circuits can be created usingstandard operational amplifier designs, with adjustable gains useful fortuning the bifurcation response. Adjustable gain and attenuation can beconveniently built into the circuit through the use of potentiometers,or alternatively, through additional multiplier elements, variable gainamplifiers (VGAs) or programmable gain amplifiers (PGAs). The option ofadding a gain or attenuating intermediate signals allows constrainingthe input ranges of the subsequent elements to avoid saturation whilemaximizing dynamic range. One method of doing this is to drive thetuning fork to resonance with a desired drive amplitude input excitation(a frequency sweep may be required to find it) and then observeintermediate signals, tuning them such that they do not saturate buttake up a significant fraction of the dynamic range of the amplifiersand multipliers.

The drive amplifier chosen should be able to drive highly capacitiveloads in a stable manner. Many operational amplifiers have maximumcapacitive loading for stable operation provided in their specificationsdata, and this should be compared to the measured impedance of thedevice being driven. The drive amplifier is configured as a summingamplifier to add together the input excitation signal and the cubicfeedback signal, which should have some option of attenuation/gaincontrol in order to tune the feedback gain.

Implementation:

The drive/summing amplifier is illustratively a LM7321 from TexasInstruments that provides for driving reactive and capacitive loads andsufficient bandwidth, and the transimpedance amplifier is illustrativelya THS4601 from Texas Instruments, a very high speed FET-input amplifier,that operates with low input bias current and high bandwidth, whichallows for a sufficient bandwidth at the operating frequency whilehaving a high transimpedance gain of 2 MΩ. The integrator and subsequentoperational amplifiers used (in the high-pass filter and for bufferamplifiers for observing signals) are illustratively OPA192 low-noiseprecision amplifiers from Texas Instruments (having sufficient bandwidthfor the tasks) and the utilized multipliers are illustratively AD633(from Analog Devices) devices. The electronics were laid out on aprinted circuit board (PCB) with multiple diagnostic outputs forobservation with an oscilloscope, including the transimpedance amplifieroutput, the integrator and high-pass filter output, the squared output,and the cubic output. Potentiometers and non-inverting amplifierscontrol the feedback gains and gains between multiplier stages, and 0.1″pitch header jumpers are used to allow the potentiometer values to bemeasured to determine the gain at the individual amplification stages.In addition, a jumper allows selection of positive, negative, or nocubic feedback into the summing amplifier. The implementation is shownin FIG. 4, with the detailed circuit diagram shown in FIG. 5. Theimplementation is provided power from a standard lab dual voltage powersupply supplying +15V, −15V, and ground. The input excitation signal isillustratively provided using an Agilent 55321 waveform generator, andthe output measurements are illustratively taken on a Agilent MSO-3104A4-channel oscilloscope. Both the waveform generator and the oscilloscopeare connected to a host PC utilizing USB, and they are correspondinglyillustratively controlled via a LabVIEW script and drivers provided byNational Instruments and Agilent.

The desired frequency response structure is produced by tuning thefeedback potentiometers, starting at the lowest gain values, and thenslowing increasing them while sweeping the frequency of the signaldriving the device.

This particular system implementation has the transimpedance boardisolated from the analog signal processing board, in order to facilitatethe use of multiple types of devices for measurement (the measureddevice is mounted to the transimpedance amplifier board along with thedrive amplifier to minimize trace length and therefore parasiticinductance, capacitance, and impedance while driving the crystal.Certain through-hole crystals (for example, Abracon Corporation ModelAB38T) and surface mount crystals (for example, Ep-son FC-135) aresupported, depending on the footprint.

Behavior is characterized by performing frequency sweeps of the inputexcitation. The output waveform (the integrator output, representing x,is measured on the oscilloscope, and the frequency, input excitationmagnitude, and output excitation magnitude are all measured using theoscilloscope with averaging of 16 waveforms, in addition to adaptivelyswitching the scale of the oscilloscope at each reading in order tomaximize resolution. Illustratively, the bifurcation frequency is in the32.700-32.800 kHz range, so a coarse sweep is initially performed withfrequency steps of 2 Hz. After a bifurcation is localized, the frequencysteps around that point are made more fine (0.1 Hz) and the frequencyrange over which measurements are taken is tightened in order to speedup the measurements. A dwell time of 3 seconds per measurement wasexemplarily used in order to allow the system to reach a steady stateafter each frequency change. The sweeps are performed both increasingand decreasing in order to appropriately characterize hysteresis. Inaddition, in a number of the examples, the magnitudes were changedbetween sweeps in order to determine the effect of input excitationmagnitude. Feedback gain was also varied in some of the tests.

To reproduce results consistently, the frequency step sizes areconsistent. A frequency jump produced by the signal generator near thebifurcation, if too large, may cause a bifurcation jump event to theother branch. A larger frequency jump will cause the system to jump moreeasily. As discussed earlier, for the disclosed example, the frequencystep was 0.1 Hz around the bifurcation point, but depending on thesensitivity of the device a lower or higher step size may beappropriate. It is also important to make certain that the function orsignal generator used to generate the excitation input should operate ina phase-continuous manner when changing frequency, as non-phasecontinuous-behavior can very briefly introduce broad-spectrumexcitation, which can cause a bifurcation event as well. In general,noise can cause the system to jump unexpectedly as well, sonoise-reduction practices such as ground planes, shielded/coaxialcabling, and relatively clean power supplies are illustratively used.The amount of noise that can be tolerated is device and applicationdependent, related to desired sensitivity of the bifurcation andfrequency resolution of excitation and measurement equipment.

The following results were generated using an Abracon Corporation modelAB38T tuning fork crystal designed for clock circuits operating at32.768 kHz.

Generation of Bifurcations and Tunability:

In order to demonstrate tunability of the response, the input excitationmagnitude was held constant at 130 mV peak-to-peak. The feedback jumperwas left unconnected so that there would be no feedback contribution tothe input excitation. Thus, the expected response is a linear one. Thenthe system was connected to negative feedback, and the systemcharacterized with two values of the feedback gain. Following this, thesystem was switched to positive feedback, and the system wascharacterized again with multiple values of the feedback gain. Theresults are plotted in FIG. 6 and demonstrate the ability of thisapproach to produce a bifurcation that can be tuned based on systemrequirements by modifying the feedback gain. In the experimentalresults, the tuning forks have a portion of the housing removed toexpose them to air. While this increases effects associated withdissipation, it is a more realistic system for the use ofbifurcation-based sensing in air. For all of the frequency responseplots in this paper, the data points represent the peak-to-peakmagnitude of the response signal, with dots representing data acquiredduring sweeps with increasing frequency, and the circles representingdata acquired during sweeps with decreasing frequency.

Repeatability experiments were performed by using three different AB38Ttuning forks (again, removed from the housing) and then performing alinear response characterization (discrete frequency sweep) with fixed75 mV peak-to-peak input excitation. The nonlinear feedback was thenconnected to the circuit with the same input excitation magnitude, andthe same feedback gain (softening) for each device. Trials with threedevices are shown in FIG. 9. The effect is repeatable with the samegains for the same devices producing a similar (though not identical)response. The responses could be made closer by tuning the gains furtherto match and compensate for device-to-device variation.

To further demonstrate the Duffing-like behavior of the system, thefeedback gain was held both a softening case (FIG. 7) and a hardeningcase (FIG. 8). In each case, the input excitation magnitude wasincreased between frequency sweeps, and the amplitude-dependent responsetypical of Duffing resonator systems is clearly present. In the case ofthe softening case, in order to have a bifurcation, it is clear that forthis particular gain (set by the potentiometer) the system requires aminimum excitation amplitude of approximately 100 mV peak-to-peak inorder to have a bifurcation. Similarly, the minimum excitation amplituderequired for bifurcation in the hardening response for this particulargain is approximately 40 mV peak-to-peak. Both of these values aregenerally within safe operational ranges for the device.

Applicability to Multiple Crystal Types: After demonstrating the methodsuccessfully with Abracon Corporation AB38T devices, an attempt was madeto determine applicability on other devices using the same circuit. AnEpson FC-135 device was soldered to the transimpedance amplifier boardin the appropriate footprint and was subjected to a softening-modefeedback with varying input amplitude, and the results, shown in FIG.10, indicate that the method is adaptable and applicable to a range ofdevices. Comparing the two devices, the FC-135 is approximately ½ to ⅓the size of the AB38T tuning fork, with significant difference in theaspect ratio of tine length to tine thickness, required to maintain thesame operating frequency. The electrode configuration and tine shapealso have some significant differences in design. The equivalent seriesresistance is also higher in the FC-135 devices (approximately 80 kΩ ascompared to approximately 40 kΩ). Despite the differences, the devicesbehave similarly enough to allow the bifurcation response to be createdon the FC-135 as well, with some tuning of feedback and internalmultiplier and filter gains.

In this disclosure, a system and circuit design is presented thatcreates a Duffing-like resonator system using off-the-shelf, relativelylow-cost components that creates an opportunity for low-costimplementation of bifurcation-based applications. The bifurcations aretunable, and are repeatable on a device to device basis for multipletypes of quartz crystal resonators. As another feature of this method,the input excitation required is significantly lower than much of theprior art when producing the bifurcation behavior.

Accordingly, at a high level, the present disclosure includes a methodincluding obtaining a first signal from a sensor having a functionalsurface layer located to interact with a material to be sensed, with thesensor having an output that produces a signal responsive one or more ofinertia, stiffness, acceleration, pressure, radiation, chemicalcompounds, and biological compounds, block 1100.

The method further includes applying one or more non-linear electricaloperations, including a first operation, to the first signal to generatea non-linear second signal, block 1110.

It should be further appreciated that while the system is described ashaving a linear sensor response provided to the processing (feedback)subsystem, embodiments are also envisioned where non-linear responsesensors are used and non-linear response signals are provided to theprocessing (feedback) subsystem.

While the present disclosure has been described with reference tocertain embodiments, it will be apparent to those of ordinary skill inthe art that other embodiments and implementations are possible that arewithin the scope of the present disclosure without departing from thespirit and scope of the present disclosure. Thus, the implementationsshould not be limited to the particular limitations described. Otherimplementations may be possible. It is therefore intended that theforegoing detailed description be regarded as illustrative rather thanlimiting. Thus, this disclosure is limited only by the following claims.

1-20. (canceled)
 21. A method for mass sensing, wherein the mass sensingcomprises: obtaining a first linear signal generated through contactinga material to be sensed with a functional surface layer of a masssensor; and applying one or more non-linear electrical operationsthrough a non-linearity feedback subsystem to said first linear signalto generate a second non-linear signal, wherein said one or morenon-linear electrical operations are capable of generating bifurcationin said second non-linear signal when said one or more non-linearelectrical operations are applied to the first linear signal.
 22. Themethod of claim 21, wherein said second non-linear signal comprisescubic non-linearity.
 23. The method of claim 21, said first linearsignal is passed through a filter subsystem before said one or morenon-linear electrical operations.
 24. The method of claim 21, whereinsaid second non-linear signal is combined with the said first linearsignal to generate a third non-linear signal, wherein said thirdnon-linear signal is adjustable through adding a gain or an attenuationof said second non-linear signal to provide a desired range of saidthird non-linear signal.